Question

The area of the region described by $A=(x,y):x^2+y^2\le 1$ and $y^2\le 1-x$ is:

• A. $\frac{\pi }{2}+\frac{4}{3}$
• B. $\frac{\pi }{2}-\frac{4}{3}$
• C. $\frac{\pi }{2}-\frac{2}{3}$
• D. $\frac{\pi }{2}+\frac{2}{3}$

Answer 1

Answer: (A)

$\frac{\pi }{2}+\frac{4}{3}$

$A=\frac{1}{2}\times \pi +2{\int }_0^1\sqrt{1-x}dx$
$=\frac{\pi }{2}+\frac{4}{3}$